The Age of Impatience … optimal replication in opportunistic networks,

2. The Age of Impatience… optimal replication in opportunistic networks, J. Reich & A. Chaintreau Thomson, Paris & Columbia U., NY Friday, September 4th, talk @ EPFL

3. How do you imagine the future Internet? Based on a vision … Interplanetary/rural/challenging environments Using all cell phones as scientific instruments Towards minimum joule per bits or Based on a true story … Social Networking Enriched Media experience Relatively short-lived content

4. How do you imagine the future Internet? (bis) Most users access content through … (1) social networking applications (2) on a mobile device. Location Location Location: “Offering a social network service that ignores location is like selling an apartment without telling where it is.” Infrastructure remains limited/expensive, while opportunistic contacts explode (BT, WiFi APs). In this talk 1 opportunistic application and some early results 3 sides: Theoretical goal, Alg. design, Practical lessons

5. Answer to pessimists: “There is no useful cellphone DTN app!” Except that current social networking is limited. “Forget it, operators will block it.” Really (android, WiMo)? reason to stop research? “Why bother, you can do it with 3G!” Perhaps, but this is cheaper. Not worth checking? “Users do not tolerate delay.” True but interface is everything BTW hard to tell (e.g., privacy)

6. Several challenges ahead! Can opportunistic contacts cope with update? Not for today (50 back-up slides available on request :) ) Can we make the right content available? Popularity profile Mobility/proximity encounters Impatience of user Can we account for impatience? Optimally?How does simple replication perform?

7. Structure of this talk Opportunistic P2P Networking P2P caching with impatient users Performance of distributed replication Future steps / concluding remarks

8. The new CTR (Click-Through-Rate) In online advertising, CTR is the probability of a click given an impression. Heavily used for sponsored search Generally used in an auction mechanism In delay tolerant network, time between a click and an impression is not negligible Delay incurs loss of revenuebecause of impatient users

9. A delay-utility measure, initialized when user request for an item : gain when request for item i is fulfilled t time later Model for impatient users

10. Model for impatient users A delay-utility measure, initialized when user request for an item : gain when request for item i is fulfilled t time later

11. Model for impatient users A delay-utility measure, initialized when user request for an item : gain when request for item i is fulfilled t time later

12. Model for impatient users A delay-utility measure, initialized when user request for an item : gain when request for item i is fulfilled t time later We assume is a non-increasing function it admits a limit when t goes to 0, (for simplicity, although all results generalize)

13. Network model The total request rate for item is It may originate from user n w.p. Network contains client nodes: Server nodes: Dedicated nodes: , Pure P2P: Rate of contacts between devices is constant Discrete time: contacts occurs during a slot w.p. Continuous time: contacts follow Poisson process

14. Cache model Let be 1 if item i is present in cache m The total number of replica is The gain perceived by the whole network is

15. Main results THM1: U submodular in x Centralized algorithm brings a 1-1/e approximation. THM2: In a homogeneous network (contacts popularity, impatience) U is a concave function Optimal reached in steps Relaxation solved by gradient descent, and optimal satisfies a balance condition

16. Sketch of the proof We introduce the differential impatience cost added loss incurred per unit of time always positive Then the expected gain when n requests i is: Balance condition: where

17. Conclusion For a general model of impatience (which may be compared to the CTR of online advertising) Network revenue maximization is submodular In addition, for homogeneous networks A unique optimal exists, satisfying balance condition

18. Structure of this talk Opportunistic P2P Networking P2P caching with impatient users Performance of distributed replication Future steps / concluding remarks

19. Optimal cache can be computed Fine, but Demands is rarely known in advances Current cache allocation is difficult to follow Different schemes available in practice Passive replication (+ public buffer) [7DS01, Podnet07] Social overlay and Utility [Yoneki07, Boldrini08] Recently, Metropolis with fraction of disseminating nodes [HuLeBoudecVojnovic09] We propose QCR to avoid maintaining explicit estimators.

20. Query-Counting Replication 1) When a request is created Counter initialized, qctr:= 0 Incremented for each request, qctr++ 2) When the demand is fulfilled Counter stopped A number (qctr) replica are made and distributed Generalizes Path replication [CohenShenker02] Has been shown to minimize search overhead With a few important differences

21. Issue #1: Tuning Query Counting Replication Approximate evolution of cache Net increase of replica for item I Demand for item i fulfilled w. p. For any replica created, replace item I w. p. Steady state satisfies balance equation iff

22. Issue #1: Tuning query counting replication Example: characterization of Power impatience =1.5 (sqrt repl.), =1 (passive repl.), =0 (~ path repl.) Opt. allocation Repl.

23. Issue #2: Mandate routing Wired p2p: data replicated along the search path Mobile p2p: replica are created in two steps 1) create set of instructions (mandates) for replication. 2) execute mandate However, step 2 relies on data availability. Solutions: Keep mandate near replicas Exchange instructions with preference to node with replica.

24. Illustration on homogeneous networks Homogeneous network Power imp. =0 Pop. Pareto(1) =5 QCR vs. alloc. Need mandate routing to converge

25. Reality test How does QCR (and others) accommodate: Heterogeneous contacts Other time statistics Traces: INFOCOM06, 50 out of 68 mobile nodes, 3 days Cabspotting, 50 out of 500 cabs, 1 typical day Comparison with perfect information channel(UNI, SQRT, PROP, DOM) and OPT

26. Infocom06 Synthetic heterogeneity & Real trace

27. Cabspotting Synthetic heterogeneous traces + real trace

28. Conclusion QCR generalizes passive and path replication can be tuned to cope with any impatience function requires mandate routing to ensure fast convergence. QCR approaches the performance of allocation built with perfect information (PROP, SQRT)

29. Structure of this talk Opportunistic P2P Networking P2P caching with impatient users Performance of distributed replication Future steps / concluding remarks

30. Structure of this talk Opportunistic P2P Networking P2P caching with impatient users Distributed blind replication Future steps / concluding remarks

31. Conclusions Can we make the right content available? Yes, with homogeneous popularity and mobility, replication adapts to serve requests timely. And, perhaps, furthermore we can 1. Cope with different interests profile / recommendation 2. Take advantage of mobility and social properties This is tractable (optimal, predictable) Promising to design new schemes We need educated fresh neurons for new interface, new platform, new algorithms, new models.

32. Sponsored ad: Call for Volunteers! The SIGMETRICS 2010 Shadow PC Between Nov-Jan, TPC meeting ~ Jan 18th Paris A unique chance to Know cutting edge works early Train at reviewing, PC meeting participation Understand how your work is judged

33. Thank you!Companion papers:- J. Reich, A. Chaintreau, “The age of impatience: optimal replication schemes for opportunistic networks” In Proc. of ACM CoNEXT, 2009 (Thomson TR CR-PRL-2009-06-0001).on the update problem:- S. Ioannidis, A. Chaintreau, L. Massoulié, “Optimal and scalable distribution of content updates over a mobile social network” In Proc. of INFOCOM, 2009.- S. Ioannidis, A. Chaintreau, “On the strength of weak ties in mobile social networks” In Proc. of ACM workshop SNS, 2009.- A. Chaintreau, J.-Y. Le Boudec, N. Ristanovic, “The age of gossip: spatial mean field model” In Proc. of SIGMETRICS/PERFORMANCE, 2009.special thanks to: S. Ioannidis, N. Ristanovic, A-K. Pietilainen, J. Lebrun, E. Oliver, C. Diot, M. May

34. 1 Application Dynamic Content frequently updated /frequently accessed Geosocial: What social networking is best at:protests (Moldova, Political Convention), disasters (Virginia Tech, Fires) Can opportunistic contacts cope with update? “As i meets j, and ages Yi < Yj then j can get i’s version.”

35. (1) P2P updates (can) scale Assumptions: A file of popular interest among users Provider pushes uniformly with rate i and j meets without memory with rate The edge expansion is THM1: how age grows as network get largers? no sharing sharing 

36. (1) Empirical results 3 Data sets (conferences, campus) Infocom06: A typical node meets every 1mn another node age: 2h -> 8mn

37. (1) What guarantees large edge expansion? 1973 hypothesis by Mark Granovetter “Our acquaintances (weak ties) are less likely to be socially involved with one another than our close friends (strong ties).” Sociological Theory, Volume 1(1983) 201-233. “Hence weak ties are essential for an individual’s integration into modern society, momentum of goal oriented task outside local circles.”

38. (1) How to manage a bandwidth budget? A peer may decide to forego some contacts: Because he or she wants to limit its bandwidth Because he or she do not trust the other peer, or do not find incentive to interact with this person Selective strategies based on contact rates: Prop Keep Lowest Rate Limit Proportional Prop Keep Highest

39. (1) Test on real topology Age remains small even with reduced bwidth. e.g. proportional. Common trends Preserving “Weak ties” is beneficial. Preserving Strong ties does not help Max. age follows edge expansion Infocom06 MIT Infocom06

40. Preliminary Conclusion (1) Opportunistic contacts to update improve age By best possible order of magnitude (lower bound) As long as edge expansion remains large Edge expansion in social networks can be large Typically in relation with the presence of weak ties. Future challenges: Different contents with varying popularity profile Incentive to assist

41. Structure of this talk Opportunistic Social Networking 1) How to characterize scalability? 2) How distribute content optimally? () An optimal distributed injection scheme () Swap of nodes ranks 3) How to model large networks? Future steps / concluding remarks

42. (2) How to measure value of dynamic data Utility as a function of content age Y Assumptions: A single piece of file, Each contact is sufficient to exchange a copy Contacts follow independent renewal Hidden markov model … a stationary ergodic process

43. (2) How to allocate downlink capacity Optimal provider: THM2: f is a concave function is the backward latency i->j hence optimal found by centralized gradient descent. Moreover No need to know ui explicitly a distributed probes scheme Hard to cheat

44. (2) Swapping the ranks of nodes Step function utility, Infocom 06 Optimal obtained for different capacity 

45. Preliminary Conclusion (2) Strategic content injection can be made optimal Even without disclosing user’s utility Importance of users depends on their centrality In reverse order for under/over capacitated network Future challenges: Optimal distribution among users Network formation Controlling energy cost [NainAltmanBermondInfocom09]

46. Structure of this talk Opportunistic Social Networking 1) How to characterize scalability? 2) How distribute content optimally? 3) How to model large networks? () Proving and Characterizing mean-field regime () Estimating impact of infrastructure Future steps / concluding remarks

47. (3) A dynamic multi-class approach Nodes belongs to a finite collection of classes C For locations, type of nodes, status, … Dynamics Mobility between classes: Update from a base station: Update from opportunistic contacts within class: between classes: Key Metric: in class c, at time t the fraction of nodes the fraction of nodes with age at most z

48. (3) “Bon sang mais c’est bien sûr!” When the network becomes large, since nodes within a class are statistically equivalent their collective behaviors becomes deterministic Mobility and age distribution converges to the solution of differential equations This reduces to an ODE “The age of gossip”

49. (3) The “Age of Gossip” Distribution The single-class case follows a closed form The multi-class follows simple asymptotic … Small age: a class belongs to one of two categories“dominant infrastructure” or “dominant opp. contacts” Large age: exponential decay that can be bounded iff

50. (3) Fast numerical estimation The importance of being spatial